When your composing text on an iPhone or iPad, it can sometimes be frustrating when you can't find the special character you need. This is especially true when typing foreign words (i.e.: mañana), but can be equally frustrating when doing something as simple as using the symbol to denote the temperature (i.e.: "88°"). On the surface, it looks like the keyboard doesn't allow for this. But alas, it does. This is how it works.
Each letter on the keyboard is capable of offering a sub-menu. This sub-menu can contain variations of the primary key. The "$" key, for example, also offers the following characters from its sub-menu: ₩, £, ¢, € and ¥. To access these additional characters, simply press and hold the "$" key. This will reveal an entirely new set of characters. From there, simply drag your finger to the new character you wish to use and let go. The degree symbol, by the way, can be found by pressing and holing on the "0" key.
As a side note, you can also add additional keyboards to your iOS device (including the ever-so-popular Emoji keyboard). To add additional keyboards, go to Settings > General > Keyboard > Keyboards.